Fibonacci Sequence in Nature and Plants.

I was so fascinated by the pictorial representation of mathematical sequences and patterns embedded in plants, flowers, trees and even in the spiral shapes of our galaxies that I felt compelled to reblog ‘plantsandbeyond’s’ post. It is my hope that you enjoy it as much as I do.

PlantsandBeyond's avatarPlants and Beyond

sunflower

The Fibonacci sequence appears in the smallest, to the largest objects in nature. It is a way for information to flow in a very efficient manner.

flower1

The actual Fibonacci sequence is this series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. Simply put, the next number in the sequence is formed by adding up the previous 2 numbers. (0 + 1 = 1, 1 + 1 = 2, 2 + 1 = 3, and so on.)

The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci. Though Fibonacci first introduced the sequence to the western world in 1202, it had been noted by Indian mathematicians as early as the sixth century.

The Fibonacci defines how the density of branches increases up a tree trunk, the arrangement of leaves on a stem, and how a pine cone’s scales are arranged. Yet you will…

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Chapter 33 of the Peter and Gertrud Klopp Story – Part III

Facing the Challenges of the English Literature Course

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University Campus with the Calgary Tower in the Background

I took some comfort in the fact that the English literature classes were small. The one I attended had only twenty students under the loving tutelage of Dr. Alexander. In my mind I called her Dr. Nightingale, because she was frequently teasing her students for not knowing the European songbird that had taken such a prominent place in John Keat’s ‘Ode to a Nightingale’. I went to see her one day after class in her office to get advice as to how to cope with my language problems. Apparently having a good knowledge of the European high school system, she pointed out that I had studied the principles of essay writing for much longer and in greater depth than my Canadian fellow students. What I would have to do was to concentrate my efforts on expanding my active and passive vocabulary and thus build up my confidence.

I became very eager to prove my ability to write well after this encouraging and heart-warming interview.  Near the end of one of the Friday morning lectures Dr. Alexander announced to the class that for Monday she planned on giving us a written test on one of two topics having to do with poems of English Romanticism. Having all weekend to prepare myself I chose the topic I felt most comfortable with, I first wrote the essay on a piece of scrap paper, then memorized the three pages sentence by sentence. When I could recite the entire text out loud, I was looking forward to take the test. All I needed to do now was to rewrite the essay from memory on the official exam paper on Monday. How proud I would feel, if I could report to Biene my first A in English 240!

Well rested and as I thought well prepared I sat at my desk in the small lecture room waiting for Dr. Alexander to come in, while others were chatting about all the fun they had had over the weekend. A bit annoyed that they were partying while I had been studying so hard, but at the same time quite relieved that with their poor preparation I would have a better chance of getting a high mark on the test, I attempted to tune them out and tried to focus on the precious content I had stored in my memory. By now I was well known to the other students for my strong, not necessarily unpleasant German accent and my often-stilted way of expressing myself. Some asked, “Well, Peter, I bet, you studied really hard for the exam.”

“I studied hard enough to get by with a passing grade,” I replied trying to be modest.

Then our professor walked in with her endearing smile. Without further ado she handed out the papers and then announced, “You will write on the second topic”, whereupon she sat down apparently quite content to spend the lecture free morning watching us write.

In the meantime I felt the emotional shockwaves of her incredible announcement racing through my mind. Believing we had a choice between the two topics, I had studied for the first one. For several minutes I stared at the blank paper in front of me. The pen I held in my right hand did not move for a very long time. Then finally I began to calm down. Under pressure and time constraints, where others would fall apart, I had the ability to make the best out of a bad situation. In a creative surge I took the parts of the memorized essay, which at least by some stretch of imagination bore some resemblance to topic two, reworded them and recombined them with ideas which I had picked up at the lectures. In spite of the initial delay I was able to hand in my finished work at the end of the fifty-minute session. With some apprehension I was awaiting the return of my paper. Great was my relief when I read the professor’s comment, ‘Well written! But very weak conclusion! 67%.’

Propelling Your Blog As The Next Hot Ticket Item

A post that every blogger striving towards excellence in blogging should read.

The Little Mermaid's avatarThe Little Mermaid

Eureka! I’ve finally discovered the secret to blogging success! The good news is that I can’t wait to share the magic potion with all of you! Whoot!

Ready?

Let’s get started…

What is ‘blogging success’ at the outset? Is it something achievable? Is it quantifiable? For me, a successful blog is one that is loved by all. A blog that is pampered in its niche attracts thousands of visitors, garners hundreds of likes and is home to a never-ending string of comments. A successul blog stands out from the rest because, well, it is amazeballs. But what does it take for an amateur to get there? Did it cross your mind at some point in time that those established bloggers were starters, like you too? Yeah? Good!

1. Passion

Passion is the key to unlock the door to blogging success. When you blog, you have to do it out of…

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Chapter 32 of the Peter and Gertrud Klopp Story – Part V

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The River Irwell at Salford, looking towards Manchester City Centre – wikipedia.org

Peter’s Passionate Plan

With the intent of giving Biene a mild shock followed by a pleasant surprise I wrote Biene  a letter, which seemed to suggest that the waiting period might be cut short by more than she had anticipated.

Calgary, September 11th 1965

My dear Biene, I have to bitterly disappoint you. Believe me, my pain is greater than yours not to see you as quickly again as we first thought possible. We must resign ourselves to some unforeseen circumstances. I don’t know how it all came about. Either the official of the university exam committee did not have all his marbles or I wasn’t quite there myself, but — I passed the test!

Aren’t you a little glad now that you will be able to come to Canada as early as next spring? Oh, how happy I am to finally have gained a foothold in Canada. This will be the last letter with my brother’s return address; for I will immediately start looking for a small apartment to rent in the northwest of Calgary close to the university. From there I will write to your parents in Velbert. I hope that they will have some understanding for our unusual plans. But I have to ask them soon, if everything related to your immigration should pan out as intended. Right after your parents have given us their consent, I will pay a visit to the immigration office and will initiate the process. You need not do anything, until the Canadian Embassy in Cologne will give you further notice and tell you what to do. Greetings with love, Peter

Biene thought she had prepared her parents well, before she had left for England. She now wrote a letter to her mother, who had given her until now her full support for our plans in Canada. In it she let her know that a letter from me would be coming soon, in which I would ask the parents to grant me permission to marry her beloved daughter. Shortly afterwards, Biene urged me, “Please write my parents soon. For now they have been prepared.”

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Manchester Town Hall – Photo Credit: wikipedia.org

In my mind, I was merely going through a number of steps that would involve a few letters going back and forth with questions about my progress at my studies, my job prospects in the teaching profession and my assurances that Biene would be well looked after and be happy. In my mind the exchange of letters was a mere formality, a remnant of an old custom that appeared antiquated in the modern world, yet had a useful function of getting to know one another. This was especially true in my case, where a formal visit from Canada was out of the question. With Biene having done her best to have her parents prepared for my letter and in view of the fact that she would be of age to determine her own destiny, I did not spend one minute worrying about a negative reply. Besides, after passing my English proficiency test, I was riding on a wave of renewed optimism and was looking forward to boldly taking on the next major hurdle, two intensive semesters back to back with hardly a break in between. My ambitious goal was not just to get by with average marks, but to excel with a high enough grade point average to be eligible for government grants to acquire the necessary financial support for the following year.

Tiny Bubbles

The post ‘Tiny Bubbles’ is about broadening our mental horizon by stepping out of our comfort zone of like-minded people and by actively seeking different perspectives, viewpoints and opinions outside our ‘tiny bubbles’. I liked the post so much that I decided to reblog it with the permission of the author Ann Coleman.

Ann Coleman's avatarMuddling Through My Middle Age

A few years ago, I passed a young woman and her dog on the sidewalk and the dog jumped up on me to say hello.  The young woman apologized, saying she had just begun to foster the dog for a rescue group and hadn’t had a chance to teach it any manners yet.  I told her it was fine, that I was a “dog person” myself and didn’t mind an enthusiastic greeting from a friendly dog.  She laughed and answered, “All my friends are dog people.  I wouldn’t be friends with anyone who wasn’t.”  I smiled politely and went on my way, but her words stuck with me.

IMG_1432I love dogs and spend a lot of time in their company, one way or another.  I share my home with a dog and I walk shelter dogs in my spare time.  Many of my good friends are dog lovers, and several…

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Chapter 31 of the Peter and Gertrud Klopp Story – Part I

At the Crossroads

“It does not take much strength to do things, but it requires a great deal of strength to decide what to do.”  Elbert Hubbard

Peter Quits his Job

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Calgary in the Mid 1960’s

In the middle of July I got an unexpected three-day break without pay. It rained so hard for the entire time that all outside construction was grinding to a halt. Restless and deeply worried I studied again the classifieds in search for a more meaningful job. There I stumbled upon an ad of a geophysical company, which was looking for young candidates whom they were willing to train with pay as seismic observers. I had not yet learned that just because there were positions to be filled and companies advertised them in the newspaper did not mean that one had already landed the job. My youthful enthusiasm for a great opportunity for carving out a happy and prosperous future for Biene and me made me ignore all the hurdles I needed to jump in order to get the job.  Nor did I heed the warnings of the somber prospects of separation, which inevitably would have come with the fieldwork in remote areas of the province. Having been apart for such a long time, this was the very thing Biene and I were trying to avoid. As always when I was all fired up and nothing in the world could dampen my zest for immediate action. I spoke with confidence and a fair level of fluency in English the day I contacted by phone the personnel manager of the company.  He appeared favourably inclined – so I thought in spite of my strong German accent – and promised me to mail right away the necessary forms and a pamphlet what seismic work was all about.

On the very same day I also visited the campus of the University of Calgary to enquire about their teachers’ training program. Here too I was impressed with the friendly and professional manner the lady at the registration booth received me. Little did I know then with my naïve trust in outward appearance that in contrast to the rough and tumble world of the construction industry these people at the institutes of higher learning were trained to be kind, helpful and polite! It was part of their job. Smug about my progress I had made in a single day I rode the bus home to my brother’s place. High in spirit, already projecting myself far into the future and seeing us in our cute little bungalow à la Biene’s vision I sat down to write her a very long passionate letter that evening, essentially pulling us out of the deep trough we had just gone through with the loss of the engagement ring.

At the beginning of the following week the blazing midsummer sun returned full blast and was burning mercilessly from a cloudless sky. Mr. Milne phoned to tell me that he would start on a new building project in the town of Vulcan, where he had taken on a lucrative contract to build a movie theatre. Knowing me as a good and reliable worker, he had assigned me to a special work crew. I found the prospect of working long hours and of making more money quite alluring at first. At five in the morning I climbed on the back of the same old truck, which had taken me to my first job site in early June. There my Yugoslav coworkers and I huddled together for the ninety-minute ride to Vulcan, halfway between Calgary and Lethbridge. The first few days turned out to be quite tolerable in spite of the heat and the long hours. The walls were still low and the heavy concrete blocks were within easy reach of the masons. Best of all the cool of the early morning air lingered on for a good part of the day. It actually felt fairly pleasant to work under such conditions, especially when a breeze brought relief from the heat in the afternoon. Yet, I was totally exhausted after fourteen hours, out which I was only paid for eleven, because they deducted the traveling time from my pay. I did not complain, the pay was good. I even had recently received a raise, which brought my weekly take-home pay to a hundred dollars. But in the second week the steadily rising walls were beginning to cut off any air circulation and the sun was relentlessly beaming down onto the building site. The masons working high up in the cool breeze were clamouring for the concrete blocks and were shouting at me to hurry up. Down in the searing furnace I struggled to keep up with the demand. With heat being reflected off the walls, the temperature was inexorably rising. I began to drink huge quantities of water and drenched my shirt in a desperate attempt to cool off the overheated body through sweating and evaporation. During such brief breaks, which I had granted myself to recuperate a little, I suddenly realized that the combined worst hardships I endured at the German army during my basic training were by comparison to this hell like a pleasant Sunday school picnic. I felt like a slave in the service of Vulcan, the god of fire, after whom the town had been named.

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Star Trek Enterprise Replica in the Town of Vulcan – Photo Credit: Wikipedia.org

While I was standing there for a short moment leaning against a huge pile of blocks, my boss caught me, as he called it, in the act of loafing and severely reamed me out. It was there and then that I decided to work only till the next payday and to start looking for another job. Unlike my fellow workers from Yugoslavia I was not a slave of this construction outfit and had the freedom to quit.